. horizontal, vertical directions in object 
coordinate system 
+ horizontal, vertical directions in a theodolite 
system 
* camera parameters 
. exterior orientation parameters of images 
. exterior orientation parameters of theodolites 
» model orientation parameters 
4.1.2. Parameters 
The primary task of bundle program is to estimate 
object coordinates and exterior orientation parame- 
ters. The functional model between object coordi- 
nates and image coordinates is the well known 
perspective transformation (Brown, 1974). In close 
range applications the parameterization of the rota- 
tion parameters is very important, because the 
chance is quite high, that some of the rotation pa- 
rameters become undeterminable. This would lead 
to the situation that the whole normal equation sys- 
tem becomes ill conditioned and the results of the 
estimation process cannot be obtained. If a bundle 
program has no special feature to handle this case 
either the program would stop or in the worst case 
it would produce wrong results. CAP utilizes a spe- 
cial estimation technique for rotation parameters 
(Hinsken, 1987; Pope, 1970). This estimation tech- 
nique combined with a special algebraic parameter- 
ization of the rotation parameters (Schut, 1958/59) 
ensures that CAP cannot have any singularity prob- 
lems due to the rotation parameters. Another effect 
of use of this technique is, that it requires minimum 
effort to compute the necessary numerical coeffi- 
cients during the iteration process. In close range 
applications where there might be lots of observa- 
tions per image this results to an overall accelera- 
tion of the adjustment process. 
For precise measurements in photogrammetry the 
camera parameters cannot considered to be known 
with sufficient accuracy beforehand. Therefore the 
bundle program has to consider the camera parame- 
ters as unknown parameters. CAP provides various 
parameters to model the camera. It is also possible 
to handle multiple cameras during one bundle ad- 
justment. For extreme cases it is possible to assign 
each image a new individual camera. This is re- 
quired for special applications with so called high 
speed drum cameras (Godding, 1990). Following 
parameters can be calibrated by CAP: 
- principal distance 
. coordinates of principal point 
» radial symmetric distortion (also dependent 
from distance between object and projection 
center) 
- asymmetric and tangential distortion 
- affinity and non orthogonality 
-  unflatness of vacuum platen 
+ irregular film deformations 
Altogether 21 parameters can be successively se- 
lected to describe the used camera. The so called 
additional parameters used in CAP are described in 
more detail in (Brown, 1976). The availability of 
the additional camera parameters makes it possible 
that CAP can be used as a special calibration tool 
for cameras. The types of cameras which can be de- 
scribed by the implemented camera model range 
from aerial cameras (Ellenbeck, Peters, 1989), large 
format close range cameras (Dold, 1990), medium 
and small format film based cameras (Peipe, 1990; 
Wester-Ebbinghaus, 1986), down to smaller format 
CCD cameras (Bósemann, Godding, Riechmann, 
1990). As it sometimes might be difficult for the 
unexperienced user to perform a so called on the 
job calibration, the camera model is implemented in 
a manner that also unexperienced users can get ap- 
propriate results. A basic difficulty with on the job 
calibration is the determinableness of the selected 
parameters. In estimation technique this problem is 
known as over and under parameterization. While 
under parameterization usually leads to non optimal 
results, over parameterization causes so called con- 
figuration defects. This means that the whole ad- 
justment system would become ill conditioned and 
would therefore deliver wrong results. To avoid this 
problem CAP utilizes special weighting technique 
of the camera parameters, so the program will al- 
ways deliver reliable results. Nevertheless the ex- 
perienced user is allowed to disable the protection 
features. 
4.1.3. Datum Definition 
A very important aspect for close range application 
is the definition of the datum of the object coordi- 
nate system. Under this topic CAP offers four ways 
of defining the datum. 
+ error free control points 
* control points with given accuracy 
. exterior orientation parameters with given 
accuracy 
+ free net adjustment 
Error free control points don't participate in the ad- 
justment they only define an error free datum. 
Control points with given accuracy participate in 
the adjustment and may be changed in the numer- 
ical values dependent on the weight with respect to 
the accuracy and strength of the image observations 
and the whole block. The quality of the datum with 
respect to accuracy depends totally on the quality 
of the control points. 
Rather seldom used but possible is the solution to 
define the datum by given exterior orientation pa- 
rameters. This requires the measurement or defini- 
tion of projection centers with respect to the object 
system. In case of a theodolite measurement the six 
exterior orientation elements of the theodolite of 
one station can be fixed to define the datum. If the 
theodolite was leveled this would lead to a leveled 
object coordinate system. The remaining degree of 
freedom can be fixed by at least one distance mea- 
surement. 
The most elegant way is to define the datum by an 
additional minimum constraint. This results in the 
so called free net adjustment. The block geometry 
must be strong enough to build a stable three di- 
mensional network. This is usually the case in close 
range app 
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